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MHT CET 2023 (10 May, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from MHT CET 2023 (10 May, Shift 2)

Q87MHT CET 2023 · 10 MAY · SHIFT 2Easy

Moment of Inertia & Radius of Gyration

The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre is Ma26\frac{Ma^2}{6}, where 'MM' is the mass and 'aa' is the side of square plate. Moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

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Answer: (b)

  1. A corner is at half the diagonal from the centre: d=a2d = \frac{a}{\sqrt{2}}, so d2=a22d^2 = \frac{a^2}{2}.
  2. Parallel axis theorem: I=Ma26+Ma22I = \frac{Ma^2}{6} + M\frac{a^2}{2}
  3. I=Ma2+3Ma26=2Ma23I = \frac{Ma^2 + 3Ma^2}{6} = \frac{2Ma^2}{3}
  4. So the answer is (b) 2Ma23\frac{2Ma^2}{3}.
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